Difference Equations 20MARKS!!

1i) Consider the difference equation
yn+1 = (3/2)(yn)^2 -1
Find the fixed points of this equation and determine whether they are linearly stable or unstable.

ii) For each fixed point Y consider the two cases y0 = Y + 0.1 and
y0 = Y -0.1 what happens to the sequence (yn)( n is some number equal or greater than zero) as n tends to infinite?


2) Explain how the Mandelbrot set can be generated by considering the behaviour of a certain difference equation in the complex numbers. Describe the fractal nature of the Mandelbrot set. Write this up in your own words please.